help me solve x(4x+6)=4?
回答 (13)
2009-07-05 4:49 am
✔ 最佳答案
x = -2x = 1/2
good luck
2009-07-05 12:34 pm
x(2x + 3) = 2
2x² + 3x = 2
x² + 3/4x = 1 + (3/4)²
x² + 3/4x = 16/16 + 9/16
(x + 3/4)² = 25/16
x + 3/4 = +/- 5/4
x = 5/4 - 3/4, x = 2/4, x = 1/2
x = - 5/4 - 3/4, x = - 8/4, x = - 2
Answer: x = 1/2, - 2
Proof (x = 1/2):
1/2(4[1/2] + 6) = 4
1/2(2 + 6) = 4
1/2(8) = 4
4 = 4
Proof (x = - 2):
- 2(4[- 2] + 6) = 4
- 2(- 8 + 6) = 4
- 2(- 2) = 4
4 = 4
2x² + 3x = 2
x² + 3/4x = 1 + (3/4)²
x² + 3/4x = 16/16 + 9/16
(x + 3/4)² = 25/16
x + 3/4 = +/- 5/4
x = 5/4 - 3/4, x = 2/4, x = 1/2
x = - 5/4 - 3/4, x = - 8/4, x = - 2
Answer: x = 1/2, - 2
Proof (x = 1/2):
1/2(4[1/2] + 6) = 4
1/2(2 + 6) = 4
1/2(8) = 4
4 = 4
Proof (x = - 2):
- 2(4[- 2] + 6) = 4
- 2(- 8 + 6) = 4
- 2(- 2) = 4
4 = 4
2009-07-05 11:55 am
This is already factored, so you need to multiply it out to solve for x. So multiply everything in the parentheses by x:
4x^2+6x=4 Now, subtract 4 from each side:
4x^2+6x-4=0 You can factor out a 2 to make it a bit easier to solve:
2(2x^2+3x-2)=0 Now factor the quadratic:
2x^2 can only be factored as x*2x, so you have (2x )(x ). The -2 can only be factored as either 2* -1 or -2 * 1, but the middle term is positive and you're multiplying one of those factors by the 2x, so lets go with 2 and -1:
(2x-1)(x+2)=0 Now, when you multiply two numbers, and the result is 0, then at least one of those numbers must be 0. So either 2x-1=0 and/or x+2=0. Solve for each:
2x-1=0 add 1 to each side:
2x=1 divide each side by 2:
x=1/2
x+2=0 subtract 2 from each side:
x= -2
So if you use either 1/2 or -2 for x, then x(4x+6) will equal 4.
4x^2+6x=4 Now, subtract 4 from each side:
4x^2+6x-4=0 You can factor out a 2 to make it a bit easier to solve:
2(2x^2+3x-2)=0 Now factor the quadratic:
2x^2 can only be factored as x*2x, so you have (2x )(x ). The -2 can only be factored as either 2* -1 or -2 * 1, but the middle term is positive and you're multiplying one of those factors by the 2x, so lets go with 2 and -1:
(2x-1)(x+2)=0 Now, when you multiply two numbers, and the result is 0, then at least one of those numbers must be 0. So either 2x-1=0 and/or x+2=0. Solve for each:
2x-1=0 add 1 to each side:
2x=1 divide each side by 2:
x=1/2
x+2=0 subtract 2 from each side:
x= -2
So if you use either 1/2 or -2 for x, then x(4x+6) will equal 4.
2009-07-05 11:49 am
4x^2 + 6x = 4
2x^2 + 3x - 2 = 0
(2x - 1)(x + 2) = 0
x = -2, 1/2
2x^2 + 3x - 2 = 0
(2x - 1)(x + 2) = 0
x = -2, 1/2
2009-07-05 5:44 pm
x(4x + 6) = 4
x(4x) + x(6) = 4
4x^2 + 6x = 4
4x^2 + 6x - 4 = 0
2(2x^2 + 3x - 2) = 0
2x^2 + 3x - 2 = 0
2x^2 + 4x - x - 2 = 0
(2x^2 + 4x) - (x + 2) = 0
2x(x + 2) - 1(x + 2) = 0
(x + 2)(2x - 1) = 0
x + 2 = 0
x = -2
2x - 1 = 0
2x = 1
x = 1/2 (0.5)
â´ x = -2, 1/2 (0.5)
x(4x) + x(6) = 4
4x^2 + 6x = 4
4x^2 + 6x - 4 = 0
2(2x^2 + 3x - 2) = 0
2x^2 + 3x - 2 = 0
2x^2 + 4x - x - 2 = 0
(2x^2 + 4x) - (x + 2) = 0
2x(x + 2) - 1(x + 2) = 0
(x + 2)(2x - 1) = 0
x + 2 = 0
x = -2
2x - 1 = 0
2x = 1
x = 1/2 (0.5)
â´ x = -2, 1/2 (0.5)
2009-07-05 1:12 pm
x(4x + 6) = 4 multiply the terms on the left
4x^2 + 6x = 4 divide both sides by 2
2x^2 + 3x = 2 subtract 2 from each side
2x^2 + 3x - 2 = 0 now factor
(2x - 1)(x + 2) = 0 set each factor equal to 0 and solve
x + 2 = 0 subtract 2 from each side gives x = -2
and 2x - 1 = 0 add 1 to each side
2x = 1 divide both sides by 2 gives x = 1/2
so you answers are x = -2 and x = 1/2
4x^2 + 6x = 4 divide both sides by 2
2x^2 + 3x = 2 subtract 2 from each side
2x^2 + 3x - 2 = 0 now factor
(2x - 1)(x + 2) = 0 set each factor equal to 0 and solve
x + 2 = 0 subtract 2 from each side gives x = -2
and 2x - 1 = 0 add 1 to each side
2x = 1 divide both sides by 2 gives x = 1/2
so you answers are x = -2 and x = 1/2
2009-07-05 12:36 pm
1/2 and -2
2009-07-05 12:11 pm
4x^2+6X-4=0
dived by 2
2x^2+3x-2 =0
( 2x -1 ) ( x+2 ) = 0
2x-1 = 0 or x + 2 = 0
2x = 1 or x = -2
x = 1/2
then x = 1/2 or x = -2
dived by 2
2x^2+3x-2 =0
( 2x -1 ) ( x+2 ) = 0
2x-1 = 0 or x + 2 = 0
2x = 1 or x = -2
x = 1/2
then x = 1/2 or x = -2
2009-07-05 12:02 pm
4 x ^ 2 + 6 x = 4
4 x ^ 2 + 6 x - 4 = 0
( 2 x + 4 ) ( 2 x - 1 ) = 0
solution1:
2 x + 4 = 0
2 x = -4
x = -2
solution 2:
2 x - 1 = 0
2 x = 1
x = 1 / 2
4 x ^ 2 + 6 x - 4 = 0
( 2 x + 4 ) ( 2 x - 1 ) = 0
solution1:
2 x + 4 = 0
2 x = -4
x = -2
solution 2:
2 x - 1 = 0
2 x = 1
x = 1 / 2
2009-07-05 11:54 am
4x^2+6x-4=0
x=[-3+&-(9+16)^1/2]/4=-2 & 1/2
x=[-3+&-(9+16)^1/2]/4=-2 & 1/2
2009-07-05 11:58 am
SOLUTION
4X^2 + 6X = 4 (YOU JUST DO DISTRIBUTIVE PROPERTY)
4X^2 + 6X -4 = 0 (IT MUST BE IN THE FORM OF A^2+B+C=0)
NOTE: 4 BECAME NEGATIVE BECAUSE OF
TRANSPOSITION OF DIGITS
(4X^2 + 8X) - (2X -4) (DO SOME FACTORING METHOD)
4X (X+2) - 2 (X+2)
(X+2) (4X - 2)
X = -2 AND X = 1/2
CHECKING: -2 {4(-2) + 6} = 4
-2 (-8+6) =4
-2 - 2 = 4
-4 =4 (IT MEANS THAT -2 IS NOT THE SOLUTION)
1/2 { 4 (1/2) + 6} = 4
1/2 ( 2 + 6) = 4
1/2 (8) = 4
4 = 4 (IT MEANS THAT 1/2 IS THE ONLY SOLUTION)
4X^2 + 6X = 4 (YOU JUST DO DISTRIBUTIVE PROPERTY)
4X^2 + 6X -4 = 0 (IT MUST BE IN THE FORM OF A^2+B+C=0)
NOTE: 4 BECAME NEGATIVE BECAUSE OF
TRANSPOSITION OF DIGITS
(4X^2 + 8X) - (2X -4) (DO SOME FACTORING METHOD)
4X (X+2) - 2 (X+2)
(X+2) (4X - 2)
X = -2 AND X = 1/2
CHECKING: -2 {4(-2) + 6} = 4
-2 (-8+6) =4
-2 - 2 = 4
-4 =4 (IT MEANS THAT -2 IS NOT THE SOLUTION)
1/2 { 4 (1/2) + 6} = 4
1/2 ( 2 + 6) = 4
1/2 (8) = 4
4 = 4 (IT MEANS THAT 1/2 IS THE ONLY SOLUTION)
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